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 A006245 Number of primitive sorting networks on n elements; also number of rhombic tilings of 2n-gon. (Formerly M1894) 17
 1, 1, 2, 8, 62, 908, 24698, 1232944, 112018190, 18410581880, 5449192389984, 2894710651370536, 2752596959306389652, 4675651520558571537540, 14163808995580022218786390 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also the number of commutation classes of reduced words for the longest element of a Weyl group of type A_{n-1} (see Armstrong reference). Also the number of oriented matroids of rank 3 on n elements (see Folkman-Lawrence reference). - Matthew J. Samuel, Jan 19 2013 Also the number of mappings X:{{1...n} choose 3}->{+,-} such that for any four indices aperm[i+2] then             swaps:=perm[i+1]:             perm[i+1]:=perm[i+2]:             perm[i+2]:=swaps:             c:=classes(convert(perm, `list`)):             sums:=sums+negs*c+classesRecurse(perm, i+2, -negs):             swaps:=perm[i+1]:             perm[i+1]:=perm[i+2]:             perm[i+2]:=swaps:             doneany:=1:         end:     end:     if spot=0 and doneany=0 then RETURN(1):     else RETURN(sums):     end: end: seq(classes([seq(n+1-i, i = 1 .. n)]), n = 1 .. 9) # Matthew J. Samuel, Jan 23 2011, Jan 26 2011 MATHEMATICA classes[perm_List] := classes[perm] = classesRecurse[perm, 0, 1]; classesRecurse[perm_List, spot_, negs_] := Module[{swaps, i, Sums, c, doneany, prm = perm}, Sums = 0; doneany = 0; For[i = spot, i <= Length[prm]-2, i++, If[prm[[i+1]] > prm[[i+2]], swaps = prm[[i+1]]; prm[[i+1]] = prm[[i+2]]; prm[[i+2]] = swaps; c = classes[prm]; Sums = Sums + negs*c + classesRecurse[prm, i+2, -negs]; swaps = prm[[i+1]]; prm[[i+1]] = prm[[i+2]]; prm[[i+2]] = swaps; doneany = 1]]; If[spot == 0 && doneany == 0, Return, Return[Sums]]]; a[n_] := a[n] = classes[Range[n] // Reverse]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 9}] (* Jean-François Alcover, May 09 2017, translated from Maple *) CROSSREFS Cf. A006246. Sequence in context: A192516 A159476 A230824 * A202751 A227160 A191604 Adjacent sequences:  A006242 A006243 A006244 * A006246 A006247 A006248 KEYWORD nonn,nice,more,changed AUTHOR EXTENSIONS More terms from Sebastien Veigneau (sv(AT)univ-mlv.fr), Jan 15 1997 a(10) confirmed by Katsuhisa Yamanaka(yamanaka(AT)hol.is.uec.ac.jp), May 06 2009. This value was also confirmed by Takashi Horiyama of Saitama Univ. a(11) from Katsuhisa Yamanaka(yamanaka(AT)hol.is.uec.ac.jp), May 06 2009 Reference with formula that the Maple program implements added and a(11) verified by Matthew J. Samuel, Jan 25 2011 Removed invalid comment concerning the denominators of the indicated polynomials; added a(12). - Matthew J. Samuel, Jan 30 2011 a(13) from Toshiki Saitoh, Oct 17 2011 a(14) and a(15) from Yuma Tanaka, Aug 20 2013 STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)